Verifiable quantum (k, n)-threshold secret sharing

Verifiable quantum (k, n)-threshold secret sharing
Yang, Yu-Guang; Jia, Xin; Wang, Hong-Yang; Zhang, Hua
2011-10-30 00:00:00
In a conventional quantum (k, n) threshold scheme, a trusted party shares a quantum secret with n agents such that any k or more agents can cooperate to recover the original secret, while fewer than k agents obtain no information about the secret. Is the reconstructed quantum secret same with the original one? Or is the dishonest agent willing to provide a true share during the secret reconstruction? In this paper we reexamine the security of quantum (k, n) threshold schemes and show how to construct a verifiable quantum (k, n) threshold scheme by combining a qubit authentication process. The novelty of ours is that it can provide a mechanism for checking whether the reconstructed quantum secret is same with the original one. This mechanism can also attain the goal of checking whether the dishonest agent provides a false quantum share during the secret reconstruction such that the secret quantum state cannot be recovered correctly.
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Abstract

In a conventional quantum (k, n) threshold scheme, a trusted party shares a quantum secret with n agents such that any k or more agents can cooperate to recover the original secret, while fewer than k agents obtain no information about the secret. Is the reconstructed quantum secret same with the original one? Or is the dishonest agent willing to provide a true share during the secret reconstruction? In this paper we reexamine the security of quantum (k, n) threshold schemes and show how to construct a verifiable quantum (k, n) threshold scheme by combining a qubit authentication process. The novelty of ours is that it can provide a mechanism for checking whether the reconstructed quantum secret is same with the original one. This mechanism can also attain the goal of checking whether the dishonest agent provides a false quantum share during the secret reconstruction such that the secret quantum state cannot be recovered correctly.